Obviously this conclusion contradicts the point of the scientists who considered the entanglement in Eq.(1) is classical entanglement [1]}, [2]}, [3]}. As we have carefully discussed above, the state in Eq.(1) is a quantum state in which the states \(\lbrace  \rho ^A_i\otimes \rho ^B_i \rbrace \)  get entangled with each other through quantum superposition, thus has quantum entanglement. Besides this point there are two other evidences to prove our conclusion. Firstly consider the three systems: A, B and C, if A gets quantum entangled with BC system group through a pure state:
\(\vert \psi _{ABC}\rangle \,=\,\sum _i\sqrt{p_i}\vert A_i B_i C_i \rangle \,,\) 
